Final answer:
The second expression, - (1/6) x (-4/9), is not equivalent to the others because it simplifies to 2/27, which is different from the value of 6 that the first and fourth expressions simplify to. The correct answer is option B .
Step-by-step explanation:
When dealing with equivalent expressions, especially those involving negative numbers or fractions, it's crucial to understand the rules of multiplication and division as they apply to positive and negative values. The question is asking which of the following expressions is not equivalent to the others:
- 1. (-4)/(-6) x (9)
- 2. - (1/6) x (-4/9)
- 3. -(4/6) x (1/9)
- 4. - (4) / (6) x (-9)
Let's simplify and compare each of the expressions step by step.
- (-4)/(-6) x (9) simplifies to 2/3 x 9, which further simplifies to 6.
- - (1/6) x (-4/9) simplifies to 1/6 x 4/9, which equals 4/54 or simplified 2/27.
- -(4/6) x (1/9) simplifies to -2/3 x 1/9, which simplifies to -2/27.
- - (4) / (6) x (-9) simplifies to -2/3 x -9, which simplifies to 6.
From our simplifications, it's apparent that the second expression, - (1/6) x (-4/9), is not equivalent to the others. Whereas the first and fourth expressions simplify to 6, the second expression simplifies to 2/27, which is a positive fraction and not equal to the others. The third expression, although similar looking in form to the second one, has one negative sign making it not positive.
Remember that when two negative numbers multiply, the answer has a +ve sign, when two numbers of opposite signs multiply, the answer has a -ve sign, and division follows similar rules concerning signs.